I couldn't find the old video of Car&Driver testing tire blowouts on Ford Explorers (Circa 2000, the suv many people were flipping into ditches after a tire failure) showing that vehicles don't automatically go turtle after a tire failure.
Police tire failure test,
YouTube - Police Blowout clip
Guy driving down the freeway (some bad language),
YouTube - Blow Out
Dodge Ram with no front tire,
YouTube - BAD DRIVER 4 miles FLAT TIRE
Now that you've seen a tire failure doesn't HAVE to be a big event lets think about it.
Newtons 2nd. An object in motion tends to stay in motion until acted apon by an outside force. A truck driving straight down the highway will continue to go straight until something forces it to turn. When a tire blows (or has too low pressure) it's rolling resistance goes up which can have a small effect and induce a pull to one side. A tire can't store enough energy to radically alter the path of a vehicle.
When a tire blows the weight it (and the tire diagonal from it) was carring is transferred to the tires across from it and the tire ahead/behind it. So now you're driving along with most of the weight of the vehicle on two good tires -that now have more grip- to keep you in control.
I should have said "loss of a single tire
doesn't have to be that big of an event". If an ordinary driver jerks the steering wheel to the right (inducing yaw) and then applies heavy braking (more yaw) and doesn't correct for the over-reaction inputs then a single tire blow out will turn into a very big event.
Back on topic; buy a trailer that is within your trucks rated limits, drive within your comfort level, scale your truck/trailer to get the weight distrubution correct (fishtailing trailers are usually too light in the nose). My 3/4ton Cummins was rated to pull my 36' race trailer but the single rear tires made for a "squishy" feeling rear end so I traded up to my dually.
As to my experience... The worst thing to happen to me due to a tire failure has been destroyed fenders/RV bay doors. My wife, my son and I all have SCCA national championships to our credit (you have to drive to a lot of big events to win the really big ones!) and I'm 15minutes from heading to the airport to fly to Marina CA to instruct at a Evolution Performance driving School.
Eric